Here again, the problem has nothing to do with a person's religion, but on a given behaviour that makes the practise of aikido in its full sense impossible. After that, if that person is a rabid supporter of the Taliban, of Torquemada or of Stalin, as long as he keeps it out of the dojo, it's not the dojo's concern anymore. After all, Ueshiba met and practised with many people with very debatable views on their nation and its place in the world.

If the person wanted to join a chess club, that no-touch rule in his/her life would not be a problem. Also, if the restriction was, for example, that s/he only dresses without anyone else in the room, it is simply an accomodation outside the core of the activity.